CN104573167B - Imperfect matching NURBS dough sheets are connected to form the computer model for being suitable for finite element analysis - Google Patents
Imperfect matching NURBS dough sheets are connected to form the computer model for being suitable for finite element analysis Download PDFInfo
- Publication number
- CN104573167B CN104573167B CN201410503337.4A CN201410503337A CN104573167B CN 104573167 B CN104573167 B CN 104573167B CN 201410503337 A CN201410503337 A CN 201410503337A CN 104573167 B CN104573167 B CN 104573167B
- Authority
- CN
- China
- Prior art keywords
- curve
- control point
- dough sheets
- group
- nurbs
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
Abstract
This application discloses for connecting imperfect matching NURBS dough sheets to form the technology for the computer model for being suitable for finite element analysis.The definition of the first and second dough sheets for linking together along physical boundary is received, physical boundary is defined in imperfect matched first curve and the second curve.The knot vector of two curves is all standardized so that parameter length is respectively equal to physical length.Curve with small number of control point is used as principal curve, another curve from curve.If curved portion is overlapped, the first and second curves are adjusted so that the first and second subpoints correspond respectively to the starting and ending position of common curve.By calculating the dependency degree from the control point of curve and the control point of principal curve, one group of linear restriction equation for connecting dough sheet along physical boundary numerical value is determined.Dough sheet and constraint equation make it possible to therefrom create the computer model suitable for finite element analysis.
Description
Technical field
Present invention relates generally to computer-aided engineering analysis, it is non-homogeneous to more particularly relate to connect imperfect matching
Reasonable basis batten (Non-Uniform Rational Basis Splines, NURBS) dough sheet is suitable for finite element fraction to be formed
Analyse the method and system of the computer model of (FEA).
Background technology
With the progress of computer technology, computer-aided engineering (CAE) and CAD (CAD) by with
The product in various industries (for example, automobile, aviation etc.) is designed in assisting engineer/scientist.A kind of CAE developed first
Technology is finite element analysis (FEA), it is to be widely used in modeling in the industry and solve and complication system (such as three dimensional non-linear
Structure design and analysis) relevant engineering problem computer approach.Geometry of the name of FEA derived from considered object
The mode being prescribed.
FEA softwares provide in model and the model (sometimes referring to FEA mesh model) of geometry description
The relevant material property each put.In this model, entity, shell of the geometry of analyzed system by various sizes
And beam indicates that they are referred to as unit.The vertex of unit is referred to as node.The model is made of the unit of limited quantity,
They are endowed title material, to associate unit with material property.Therefore the model indicates analyzed object
Along the physical space occupied by the environment around it.Then FEA softwares refer to table, in the table each material type
Characteristic (for example, stress-strain constitutes equation, Young's modulus, Poisson's ratio, thermal conductivity) is made as table.In addition, alsoing specify
The boundary condition (it is, load, physical constraint etc.) of object.In this way, the model of object and its environment is created.
In addition, the industry for being referred to as CAD (CAD) is developed for indicating the geometry of product, such as
Surface modeling.In CAD, the curve for being based primarily upon NURBS and surface have been used.In general, the design of product is encapsulated in CAD systems
In system, and FEA mesh model is generated from CAD data.Therefore, FEA mesh model is indicated by the approximate geometry of product.Usually
The generation of such FEA mesh model is executed using semi-automatic mode.In order to overcome these defects, has developed and be based on
The FEA of NURBS.
Since the difference of CAD and FEA requires, have the shortcomings that related to the FEA based on NURBS.One of disadvantage
It is related to NURBS surface descriptions are cut out.Particularly, the regular surfaces NURBS that the surfaces NURBS include lower layer are cut out, there is definition
The additional cut line that the surface patches of lower layer are shown or are not displayed.Although cutting out NURBS operational excellences in CAD,
Be its use in FEA it is still theme in current research, is not state-of-the-art.Instead of directly being cut out using original
NURBS indicates that it can will be cut into one group smaller of regular NURBS dough sheets first.Next it is necessary for the smaller rule
NURBS dough sheets create one group of new NURBS parameter, to be suitable for FEA (for example, maintaining the continuity at patch boundaries).But
Create the task that one group of NURBS parameter is tediously long and difficult.
Therefore, it is desirable to be useful for connecting imperfect matching NURBS dough sheets to form the computer mould for being suitable for finite element analysis
The method and system of type.
Invention content
This part is for summarizing certain aspects of the invention and briefly introducing some preferred embodiments.It can be to herein
This part and abstract and title, which are made, to be simplified and omits, and becomes unobvious to avoid the purpose for making this part.Such letter
Change or omit the range being not intended to restrict the invention.
This application discloses for connecting imperfect matching NURBS dough sheets to form the computer mould for being suitable for finite element analysis
The method and system of type.According to an aspect of the present invention, determining for the first and second NURBS dough sheets is received in computer systems
Justice.First and second NURBS dough sheets will link together along physical boundary, physical boundary the first dough sheet the first curve and
Defined in second curve of the second dough sheet, there is the first curve first group of control point, first group of control point to have relevant weight
With corresponding first node vector；Second curve has second group of control point, and second group of control point has relevant weight and right
The second node vector answered.First curve and the second curve are using different control points, weight and knot vector definition.Two songs
The knot vector of line is standardized so that parameter length is respectively equal to physical length.
Indicate that the common curve of physical boundary is determined.The common curve can be between the first curve and the second curve
Lap.Next, adjustment (for example, bi-directional scaling and displacement) first and second curve node is sweared in the following ways
Magnitude：Setting u=0 will obtain subpointU=L is setcIt will obtain subpoint(with reference to Fig. 7 C-7E).In overlapping portion
The curve with small number of control point is divided to be designated as principal curve, another curve is designated as from curve.
By calculating the dependency degree from the control point of curve and the control point of principal curve, obtain for along physical boundary number
One group of linear restriction equation of value the first and second NURBS dough sheets of connection.Dough sheet and along physical boundary this group constraint equation
Together so that the computer model therefrom created is suitable for finite element analysis.
Principal curve is used according to another aspect, and removes technology or selection with virtual from the virtual insertion between curve
Dependency degree is determined using the pseudoinverse of S shown in Fig. 7 F to property.
Pass through the detailed description below in conjunction with attached drawing to specific implementation mode, other objects of the present invention, feature and advantage
It will become apparent.
Description of the drawings
With reference to description, appended claims and attached drawing below, it will more fully understand these and other of the present invention
Feature, aspect and advantage, wherein：
Figure 1A -1C collectively illustrate according to an embodiment of the invention for connecting imperfect matching NURBS dough sheets with shape
At the flow chart of the example procedure of the computer model suitable for finite element analysis；
Fig. 2 is the exemplary NURBS dough sheets according to an embodiment of the invention to link together along physical boundary
Schematic diagram；
Fig. 3 A-3B are the schematic diagrames of exemplary partly overlapping NURBS dough sheets according to an embodiment of the invention；
Fig. 4 is the imperfect matching NURBS dough sheets of two demonstrations according to an embodiment of the invention and their correlation
The plan view at control point and knot vector；
Fig. 5 A-5C are the exemplary schematic diagrames for creating control point dependency degree according to an embodiment of the invention；
Fig. 6 A-6B are the demonstrations according to an embodiment of the invention created using example procedure shown in Figure 1A -1B
The schematic diagram of computer model；
Fig. 7 A-7F are the imperfect matchings to be linked together using exemplary method according to an embodiment of the invention
A series of schematic diagrames of NURBS dough sheets；And
Fig. 8 is the functional block diagram of the primary clustering of computer system, and the embodiment of the present invention can be in the computer system
Implement.
Specific implementation mode
In the following description, many special details are listed, to provide a thorough understanding of the present invention.But for
For those skilled in the art, it is evident that the present invention can be carried out without these specific details.Description herein
It is the conventional means of those skilled in the art with expression, this field is communicated to for the essence most effectively by their effect
Technical staff.In other examples, it is not described in known method, program and component, to avoid unnecessarily making
Certain aspects of the invention become unobvious.
" one embodiment " or " embodiment " mentioned herein means the specific feature with reference to embodiment description, knot
Structure or feature can be included at least one embodiment of the invention.Phrase in specification everywhere " is implemented at one
Example in " appearance need not all refer to identical embodiment, nor repel other embodiment independent or selective reality
Apply example.In addition, indicate one or more embodiments of the invention process flow diagram flow chart or the box in schematic diagram sequence simultaneously
It does not indicate any specific sequence in the present invention inherently or implies any restrictions.
The embodiment of the present invention will be discussed A-8 referring to Fig.1 herein.But it will be appreciated by a person skilled in the art that herein
With reference to the detailed description that these attached drawings provide be for explanation purposes, the present invention may extend into these limitation embodiment it
Outside.
With reference first to Figure 1A -1C, collectively illustrate according to an embodiment of the invention for connecting imperfect matching
NURBS dough sheets are to form the flow chart of the example procedure 100 for the computer model for being suitable for finite element analysis.Process 100 is preferred
Ground is implemented in software, and is understood with reference to other accompanying drawings, such as Fig. 2-8.
Process 100 starts from step 102, is equipped with the computer system of application module on it (for example, the calculating of Fig. 8
Machine 800) in receive the first and second NURBS dough sheets definition.The application module can be for creating having based on NURBS
The software of finite element analysis computer model.Sometimes, software for the purpose is referred to as preprocessor (for pre-processing input
File makes it become appropriate for project analysis (such as finite element analysis)).As shown in Fig. 2, the first and second NURBS dough sheets 202-
204 will link together along physical boundary 210 (for example, physical curve or shared curve).Physical boundary 210 is first
Defined in first curve 212 of NURBS dough sheets 202 and the second curve 214 of the 2nd NURBS dough sheets 204.First curve 212 by
First group of control point, their associated weight and corresponding first group node vector value indicate that the second curve 214 is by second group of control
Point, their associated weight and corresponding second group node vector value processed indicate.According to an aspect of the present invention, the first curve
212 and second curve 214 be variously defined, but identical physical boundary 210 is indicated in certain margin of tolerance.In other words
It says, the first curve 212 and the second curve 214 are part matchings or imperfect matched.Tolerance can be by the use of application module
Family provides or adopts to define inside application module by known method.
Next, in step 104, the knot vector value of the first curve is standardized so that parameter length is equal to its object
Manage length.Similarly, in step 106, the knot vector value of the second curve is standardized.The exemplary journey of one of standardized curve
Sequence is the physical length (for example, passing through numerical integration) of calculated curve first, then indicates the knot vector of curve by proportion
Scaling so that the difference matching physical length between first and last knot vector value.
In step 111, the common curve (or shared curve) for indicating physical boundary is determined.The common curve can be
Lap between first and second curves.Two exemplary partly overlapping NURBS dough sheets are shown in Fig. 3 A-3B.
Next, in step 112, it is bent that (for example, bi-directional scaling and displacement) first and second is adjusted in the following ways
Line knot vector value：Setting u=0 will obtain subpointU=L is setcIt will obtain subpoint(with reference to Fig. 7 C-7E).
In other words, as adjustment as a result, the first and second subpoints correspond respectively to the starting and ending position of common curve.
Following step 113, has one in first and second curves at small number of control point along lap
A to be designated as principal curve, another is designated as from curve.Fig. 4 is shown along two that physical boundary 410 links together
The schematic diagram of plasticity NURBS dough sheets 402-404, is respectively provided with the first curve 412 and the second curve 414.First curve 412 is by
One group of control point 422 (hollow dots) definition, the second curve 414 are defined by second group of control point 424 (solid dot).First curve
412 are designated as principal curve, and the second curve 414 is designated as from curve, because having small number of control in the first curve 412
Point processed.
Finally, in step 114, determine along physical boundary numerical value connect one group of the first and second NURBS dough sheets it is linear
Constrain equation.The control point (independent control point) of the constraint equation based on principal curve and the control point from curve (rely on control
Point) between dependency degree.Equation is constrained using this group to limit the displacement from curve to principal curve, the first and second NURBS
Dough sheet can unanimously be deformed along common physical boundary.Dependency degree can calculate as follows：By executing from altogether in step 114a
With curve to first group of one or more knot vector insertion operation from curve, the first dependence is determined；In step 114b
In by executing second group of one or more knot vector insertion operation from common curve to principal curve, determine that the second dependence is closed
System；And linear restriction equation is calculated from the first and second dependences in step 114c.
First and second NURBS dough sheets and along the control point of physical boundary constraint equation therefrom to create it is suitable
In the computer model of finite element analysis.
In order to which how calculated dependency degree of demonstrating is, Fig. 5 A-5C show a series of attached drawing.As shown in Figure 5A, main
Curve 502 is defined by one group of Master Node 522 (being shown with dot) and corresponding knot vector value 512 (being shown as " | "), from curve
504 are defined by one group from control point 544 (being shown with triangle) and corresponding knot vector value 514 (being shown as " X ").For determination
From the control point of curve 544 to the dependency degree at the control point 522 of principal curve, there are two steps：Dummy node vector value be inserted into and
Dummy node vector value removes.
In virtual node vector insertion procedure, be not be included in it is any from curve in the knot vector of principal curve
Knot vector value be all virtually inserted into the knot vector of principal curve.The dependency degree for the knot vector value being virtually inserted into is counted
It calculates.It is not that the knot vector value 516 of the slave curve being included in principal curve is inserted into principal curve 502 that Fig. 5 B, which are shown,
In.The Control point 526 for the knot vector value 516 being inserted into is converted into new control point 532 (being shown with open circles).
In this example, there are two from the knot vector value 516 of curve not in principal curve.For other situations, may be present
The control point of other quantity.
After the insertion of dummy node vector has been carried out, knot vector removal is performed for removing not from curve
In any principal curve knot vector value.The dependency degree of the knot vector value virtually removed is calculated later.As shown in Figure 5 C, it saves
Point vector value 518 is removed, and two corresponding control points 538 are converted into a control point 542 (being shown with grey dot).It needs
It should be noted that knot vector value 518 is not present in from curve.The control point 522,532,542 of obtained principal curve with from
The control point 544 of curve is identical.
Fig. 6 A-6B show according to an embodiment of the invention using the connection NURBS dough sheets of process 100 showing to establishment
Plasticity computer model.In this example, it creates with porose regular dough sheet.
First, the regular NURBS dough sheets 602 in no hole 610 are defined.Next one group removed at 610 place of hole is " single
Member " 604.Finally, it is defined around one group of dough sheet 612 in hole 610, and along boundary and there is one group of removed unit
Dough sheet connect.Control point 622 is indicated along " X " on boundary.Process 100 shown in Figure 1A -1C can be used come the company of completion
Connect two dough sheets.
Referring now to Fig. 7 A-7F, shows to be joined together to form along physical boundary (" common curve " 715) and be suitable for
Two exemplary imperfect matching NURBS dough sheets (" dough sheet -1 " 701 and " dough sheet -2 " 702) of the computer model of FEA.
" common curve " 715 is the lap between the first curve " curve -1 " 711 and the second curve " curve -2 " 712." curve-
1 " 711 and " curve -2 " 712 be respectively " dough sheet -1 " 701 and " dough sheet -2 " 702 boundary curve.In addition, " curve -1 " 711 by
Control pointDefinition, " curve -2 " 712 is by control point
Definition.
All curves are all by the knot vector at control point and control point, polynomial order and weight definition
Nurbs curve.Typical pth degree nurbs curve is defined as follows by equation (1)：
Wherein：
(n+1) be control point quantity；
(m+1) be node quantity (m=n+p+1)；
PiIt is control point；
wiIt is control point PiThe weight at place；
P is the polynomial order (degree) of curve；
U(u0,u1,..,um) it is knot vector, include the nondecreasing sequence of real number；
Ni,p(u) it is pth degree B-spline basic function (recursively defining)；
Following curve is standardized so that parameter length is equal to physical length.It is bent in order to calculate NURBS shown in Fig. 7 B
The length L 720 of line 710 has used equation below (2)-(4).
L=Lp+...+Lm-1-p (3)
Once the respective arc length of two curves (it is, " curve -1 " 711 and " curve -2 " 712) is calculated,
With regard to two knot vectors of bi-directional scaling and displacement.Such as the start node vector of curve be listed in U=(a ..., a,
up+1,...,um-p-1,b,...,b).There are (p+1) item " a " and " b ".Arc length is calculated using equation (5).
Referring now to Fig. 7 C, the subpoint on " curve -1 " 711 and " curve -2 " 712 is respectively illustratedWithThis two
The starting and ending of a point label lap (or common curve 715).Standardized knot vector is shifted as follows：
0 is located atPlace, Lc=b1=a2It is located atPlace.LcIt is the arc length of common curve 715.In this example, only " curve-
1 " 711 standardization knot vector is shifted "-a1”.Therefore, each knot vector of " curve -1 " 711 and " curve -2 " 712WithIt indicates as follows：
Next, along lap (common curve 715) there is the curve at less control point to be designated as principal curve.Separately
One curve is designated as from curve.In the example shown in Fig. 7 D, " curve -1 " 711 is designated as from curve, and " curve -2 "
712 are designated as principal curve, because along the lap 715 of " curve -2 " 712 there are four control point, and " curve -1 " 711
There are six control points.The knot vector of " curve -1 " 711 is
The knot vector of " curve -2 " 712 is
In addition, the method for showing node insert operation in the following examples：
NodeIt is inserted into knot vector u=[u1,u2,...,um] in.
Then calculating ratio is as follows：For k-p+1≤i≤k,
Next it is inserted into the control point of weightingIt is as follows：
According to one aspect, the present invention relates to one or more computer systems that can perform function described here.It calculates
The example of machine system 800 is shown in FIG. 8.Computer system 800 includes one or more processors, such as processor 804.Place
Reason device 804 is connected to inside computer system communication bus 802.About the exemplary computer system, there are various softwares real
Existing description.After running through this description, the personnel of correlative technology field will be appreciated that if using other computer systems and/
Or computer architecture implements the present invention.
Computer system 800 further includes main memory 808, preferably random access memory (RAM), may also include auxiliary and deposits
Reservoir 810.Additional storage 810 includes that for example one or more hard disk drives 812 and/or one or more can be removed store
Driver 814, they represent floppy disk driver, tape drive, CD drive etc..Removable memory driver 814
It is written in a known manner from reading in removable storage unit 818 and/or into removable storage unit 818.It can be removed and deposit
Storage unit 818 represents can be by floppy disk, tape, CD etc. that removable storage drive 814 reads and writees.It is appreciated that
Removable storage unit 818 includes being stored thereon with the computer readable medium of computer software and/or data.
In an alternative embodiment, additional storage 810 may include other similar mechanism, allow computer program or its
It instructs and is loaded onto computer system 800.Such mechanism includes such as removable storage unit 822 and interface 820.In this way
Example may include program cartridge and cartridge interface (for example, those of in video game device), can be removed
Storage chip (such as erasable programmable read only memory (EPROM)), universal serial bus (USB) flash memory or PROM)
And relevant slot and other removable storage units 822 and software and data is allowed to be passed from removable storage unit 822
It is delivered to the interface 820 of computer system 800.In general, computer system 800 is controlled and is managed by operating system (OS) software, behaviour
Make system and executes such as process scheduling, memory management, network connection and I/O services.
The communication interface 824 for being connected to bus 802 may be additionally provided with.Communication interface 824 allows software and data calculating
It is transmitted between machine system 800 and external equipment.The example of communication interface 824 includes modem, network interface (such as ether
Network interface card), communication port, Personal Computer Memory Card International Association (PCMCIA) slot and card etc..Computer 800 is based on one group
Specific rule (it is, agreement) passes through data network and other computing device communications.The one of which of puppy parc be
General TCP/IP (transmission control protocol/Internet protocol) in internet.In general, communication interface 824 combines data file
Smaller data packet is processed by data network transmission, or the data packet received is reassembled into original data text
Part.In addition, communication interface 824 handles the address part of each data packet so that it reaches correct destination, or midway section
Take the data packet for being sent to computer 800.In this part of file, term " computer program medium " and " computer available media " are all
It is used to refer to for medium, such as removable storage drive 814 and/or the hard disk that is arranged in hard disk drive 812.These are calculated
Machine program product is the means for providing software to computer system 800.The present invention relates to the productions of such computer program
Product.
Computer system 800 further includes input/output (I/O) interface 830, it makes computer system 800 have access to
Display, keyboard, mouse, printer, scanner, draught machine and similar devices.
Computer program (also referred to as computer control logic) as application module 806 be stored in main memory 808 with/
Or in additional storage 810.Also computer program can be received by communication interface 824.Such computer program is performed,
So that computer system 800 executes the feature of the present invention as discussed in this.Particularly, when executing the computer program,
So that processor 804 executes the feature of the present invention.Therefore, such computer program represents the controller of computer system 800.
In embodiment of the present invention using software realization, which is storable in computer program product, and can make
It is loaded into computer system 800 with removable storage drive 814, hard disk drive 812 or communication interface 824.Using
When module 806 is executed by processor 804 so that processor 804 executes the function of the present invention as described herein.
Main memory 808 can be loaded one or more application module 806, and the application module 806 can be by one or more
A processor 804 executes to realize desired task, and the processor can be with or without being inputted by I/O interfaces 830
User inputs.In operation, it when at least one processor 804 executes an application module 806, is as a result computed and stored in
In additional storage 810 (it is, hard disk drive 812).The result (for example, principal curve and dependency degree from curve) of calculating
According to user instruction, by word or it is figured in a manner of by I/O interfaces 830 report to user.
Although with reference to specific embodiment, invention has been described, these embodiments be only it is explanatory,
It is not intended to restrict the invention.Those skilled in the art can be implied, be made respectively to specifically disclosed exemplary embodiment
Kind modifications and changes.Although for example, the first and second NURBS dough sheets are shown using rectangle plane view, in the present invention
In identical purpose can also be realized using other shapes.In addition, although Fig. 5 A-5C show the example of arbitrary simplification,
It is the present invention to the not restriction of control point/knot vector value in any NURBS dough sheets/curve.In short, the scope of the present invention is not
It is limited to particular exemplary embodiment disclosed herein, all modifications implied for those skilled in the art will be all included in
In the range of spirit and scope and appended claim.
Claims (12)
1. a kind of being suitable for finite element analysis for connecting imperfect matching non-uniform rational basis batten NURBS dough sheets to be formed
The method of computer model, which is characterized in that the method includes：
The definition that the first NURBS dough sheets and the 2nd NURBS dough sheets is received in the computer system of application module is installed on it,
The first and second NURBS dough sheets link together along physical boundary, the physical boundary in the first NURBS dough sheets
Defined in second curve of one curve and the 2nd NURBS dough sheets, first curve has first group of control point, relevant weight
With more than corresponding first a knot vector values；Second curve has second group of control point, relevant weight and corresponding the
A knot vector value more than two, wherein first group of control point and more than first a knot vector value and second group of control
Point is different with more than described second a knot vector values；
By more than described first a knot vector value standardization so that the parameter of the first curve described in the first NURBS dough sheets
Length is equal to the physical length of first curve；
By more than described second a knot vector value standardization so that the parameter of the second curve described in the 2nd NURBS dough sheets
Length is equal to the physical length of second curve；
Determine common curve be first and second curve lap to indicate the physical boundary；
Adjust first and second curve so that the first and second subpoints correspond respectively to the common curve starting and
End position；
Specify in first and second curve has one of small number of control point as master along the common curve
Curve, another one are used as from curve；And
By calculating the dependency degree from the control point of curve and the control point of principal curve, determine for connecting along physical boundary numerical value
Connect one group of linear restriction equation of the first and second NURBS dough sheets, to the first and second NURBS dough sheets and along
One group of linear restriction equation at the control point of the physical boundary makes it possible to therefrom create the meter suitable for finite element analysis
Calculation machine model.
2. according to the method described in claim 1, it is characterized in that, the control calculated from the control point of curve and principal curve
Point dependency degree further include：
By determining the first dependence from common curve to from the first group node insertion operation of curve；
The second dependence is determined by the second group node insertion operation from common curve to principal curve；And from described first
One group of linear restriction equation is calculated with the second dependence.
3. according to the method described in claim 1, it is characterized in that, one group of linear restriction equation numerical value constrains the calculating
The modal displacement at the control point from the modal displacement at the control point of curve dependent on the principal curve in machine model.
4. according to the method described in claim 1, it is characterized in that, the application module is for creating the computer model.
5. according to the method described in claim 1, it is characterized in that, the physical boundary is provided by user.
6. according to the method described in claim 5, it is characterized in that, first curve and the second curve are from the physics side
It is approximate in the margin of tolerance that boundary measures.
7. a kind of being suitable for finite element analysis for connecting imperfect matching non-uniform rational basis batten NURBS dough sheets to be formed
The system of computer model, which is characterized in that the system comprises：
Input/output interface；
Memory, the computer-readable code for storing application module；
At least one processor being connected with the memory, at least one processor execute the calculating in the memory
Machine readable code so that the application module executes following operation：
The definition of the first NURBS dough sheets and the 2nd NURBS dough sheets is received, the first and second NURBS dough sheets are along physics side
Boundary links together, and the physical boundary is in the first curve of the first NURBS dough sheets and the second curve of the 2nd NURBS dough sheets
Definition, first curve have first group of control point, relevant weight and corresponding more than first a knot vector value；Described
Two curves have second group of control point, relevant weight and corresponding more than second a knot vector value, wherein first group of control
System point and more than first a knot vector value are different from second group of control point and more than second a knot vector value；
By more than described first a knot vector value standardization so that the parameter of the first curve described in the first NURBS dough sheets
Length is equal to the physical length of first curve；
By more than described second a knot vector value standardization so that the parameter of the second curve described in the 2nd NURBS dough sheets
Length is equal to the physical length of second curve；
Determine common curve be first and second curve lap to indicate the physical boundary；
Adjust first and second curve so that the first and second subpoints correspond respectively to the common curve starting and
End position；
Specify in first and second curve has one of small number of control point as master along the common curve
Curve, another one are used as from curve；And
By calculating the dependency degree from the control point of curve and the control point of principal curve, determine for connecting along physical boundary numerical value
Connect one group of linear restriction equation of the first and second NURBS dough sheets, to the first and second NURBS dough sheets and along
One group of linear restriction equation at the control point of the physical boundary makes it possible to therefrom create the meter suitable for finite element analysis
Calculation machine model.
8. system according to claim 7, which is characterized in that the control calculated from the control point of curve and principal curve
Point dependency degree further include：
By determining the first dependence from common curve to from the first group node insertion operation of curve；
The second dependence is determined by the second group node insertion operation from common curve to principal curve；And
One group of linear restriction equation is calculated from first and second dependence.
9. system according to claim 7, which is characterized in that one group of linear restriction equation numerical value constrains the calculating
The modal displacement at the control point from the modal displacement at the control point of curve dependent on the principal curve in machine model.
10. system according to claim 7, which is characterized in that the application module is for creating the computer model.
11. system according to claim 7, which is characterized in that the physical boundary is provided by user.
12. system according to claim 11, which is characterized in that first curve and the second curve are from the physics
It is approximate in the margin of tolerance of boundary survey.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US14/051,559 US20150106065A1 (en) | 2013-10-11 | 2013-10-11 | Joining Imperfectly-Matching NURBS Patches To Form a Computerized Model Suitable For FEA |
| US14/051,559 | 2013-10-11 |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104573167A CN104573167A (en) | 2015-04-29 |
| CN104573167B true CN104573167B (en) | 2018-09-14 |
Family
ID=52810378
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201410503337.4A Active CN104573167B (en) | 2013-10-11 | 2014-09-26 | Imperfect matching NURBS dough sheets are connected to form the computer model for being suitable for finite element analysis |
Country Status (2)
| Country | Link |
|---|---|
| US (2) | US20150106065A1 (en) |
| CN (1) | CN104573167B (en) |
Families Citing this family (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2017142953A1 (en) * | 2016-02-16 | 2017-08-24 | Board Of Regents, University Of Texas System | Mechanisms for constructing spline surfaces to provide inter-surface continuity |
| US10810795B2 (en) * | 2018-06-13 | 2020-10-20 | S-Splines, LLC | Isogeometric analysis and computer-aided design using S-splines |
| WO2020122882A1 (en) | 2018-12-11 | 2020-06-18 | Hewlett-Packard Development Company, L.P. | Determination of vertices of triangular grids for three-dimensional object representations |
| US11684192B2 (en) | 2019-03-25 | 2023-06-27 | Jason Kraning | Presentation system having static and dynamic components |
| CN110039538B (en) * | 2019-04-03 | 2020-12-08 | 华中科技大学 | Robot track planning method based on large complex component point cloud information |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1849608A (en) * | 2003-07-16 | 2006-10-18 | 独立行政法人理化学研究所 | Method and program for generating volume data from boundary representation data |
| CN101110127A (en) * | 2006-07-21 | 2008-01-23 | 达索系统公司 | Computer-implemented process for creating a parametric surface |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2008037819A2 (en) * | 2006-09-29 | 2008-04-03 | Airbus España, S.L. | Method and system for designing smooth surfaces for vehicle parts |
| WO2009012370A1 (en) * | 2007-07-19 | 2009-01-22 | Board Of Regents, The University Of Texas System | Method and system for performing t-spline based isogeometric analysis |
| US20150127301A1 (en) * | 2013-11-05 | 2015-05-07 | Spatial Corporation | Updating A CAD Model To Reflect Global Or Local Shape Changes |
-
2013
- 2013-10-11 US US14/051,559 patent/US20150106065A1/en not_active Abandoned
-
2014
- 2014-09-26 CN CN201410503337.4A patent/CN104573167B/en active Active
-
2017
- 2017-12-20 US US15/847,919 patent/US20180129764A1/en not_active Abandoned
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1849608A (en) * | 2003-07-16 | 2006-10-18 | 独立行政法人理化学研究所 | Method and program for generating volume data from boundary representation data |
| CN101110127A (en) * | 2006-07-21 | 2008-01-23 | 达索系统公司 | Computer-implemented process for creating a parametric surface |
Non-Patent Citations (3)
| Title |
|---|
| A finite volume method on NURBS geometries and its application in isogeometric fluid–structure interaction;Ch. Heinrich et al;《Mathematics and Computers in Simulation》;20120419;第1645-1666页 * |
| NURBS曲面Gl光滑拼接算法;周西军等;《计算机辅助设计与图形学学报》;19960531;第8卷(第3期);第227-233页 * |
| 改进的非均匀有理Ｂ样条曲面片拼接算法;吴禄慎等;《光学精密工程》;20130228;第21卷(第2期);第431-436页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104573167A (en) | 2015-04-29 |
| US20150106065A1 (en) | 2015-04-16 |
| US20180129764A1 (en) | 2018-05-10 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN104573167B (en) | Imperfect matching NURBS dough sheets are connected to form the computer model for being suitable for finite element analysis | |
| US10613496B2 (en) | Support structure constrained topology optimization for additive manufacturing | |
| JP7049072B2 (en) | Modeling and analysis of leading edge ribs on aircraft wings | |
| US10915675B2 (en) | Structural optimization of additively manufactured parts accounting for manufacturing-induced states | |
| CN110059330B (en) | Method and system for authoring simulated scenes | |
| KR102544597B1 (en) | Methods and systems for simulating structural behaviors of reinforced concrete in finite element analysis | |
| CA2667334C (en) | Method and devices for aiding in the modeling of 3d objects | |
| US20150127301A1 (en) | Updating A CAD Model To Reflect Global Or Local Shape Changes | |
| EP3118817B1 (en) | Post-processing system for finite element analysis | |
| EP2669827A2 (en) | Numerical simulation of a structure having a heat-affected zone using a finite element analysis model | |
| US20110282637A1 (en) | Numerical simulation of airflow within porous materials | |
| US9495798B2 (en) | Method and device for producing a finite element model | |
| CN107066646A (en) | Topologies change in affined asymmetric subdivided meshes | |
| EP2357578A1 (en) | Multiscale substructures in finite element analysis | |
| CN108133084A (en) | A kind of quality of data inspection method, device, controller and system | |
| Petsch et al. | PANDORA-A python based framework for modelling and structural sizing of transport aircraft | |
| US20110208497A1 (en) | Computer aided design method for creating a surface in a complex system | |
| CN117217049A (en) | Finite element analysis preprocessing method and system based on Ploughmesh | |
| Ali et al. | Efficient preprocessing of complex geometries for CFD simulations | |
| US20170116360A1 (en) | Efficient explicit finite element analysis of a product with a time step size control scheme | |
| US20190258763A1 (en) | Methods And Systems For Manufacturing Products/Parts Made Of Carbon Fiber Reinforced Composite Based On Numerical Simulations | |
| Shepherd et al. | Hexahedral mesh generation for biomedical models in SCIRun | |
| KR100666789B1 (en) | System and method thereof creating computer aided engineering model using computer aided design model of ship created by hull structure detail design stage | |
| US20160078161A1 (en) | Structural Topology Optimization Using Numerical Derivatives | |
| US11347911B2 (en) | Systems and methods of determining a numerical material model that optimally emulates physical material test results |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |